# Stored data for newform 448.8.a.h, downloaded from the LMFDB on 11 March 2026.
{"Nk2": 28672, "analytic_conductor": 139.94849141688655, "analytic_rank": 0, "analytic_rank_proved": true, "atkin_lehner_eigenvals": [[2, -1], [7, -1]], "atkin_lehner_string": "--", "char_conductor": 1, "char_degree": 1, "char_is_minimal": false, "char_is_real": true, "char_orbit_index": 1, "char_orbit_label": "a", "char_order": 1, "char_parity": 1, "char_values": [448, 1, [127, 197, 129], [1, 1, 1]], "cm_discs": [], "conrey_index": 1, "dim": 1, "field_disc": 1, "field_disc_factorization": [], "field_poly": [0, 1], "field_poly_is_cyclotomic": false, "field_poly_is_real_cyclotomic": false, "field_poly_root_of_unity": 0, "fricke_eigenval": 1, "has_non_self_twist": 0, "hecke_cutters": [[3, [-46, 1]]], "hecke_orbit": 8, "hecke_orbit_code": 31525197525811648, "hecke_ring_generator_nbound": 1, "hecke_ring_index": 1, "hecke_ring_index_factorization": [], "hecke_ring_index_proved": true, "inner_twist_count": 1, "inner_twists": [[1, 1, 1, 1, 1, 1, 1]], "is_cm": false, "is_largest": false, "is_maximal": false, "is_polredabs": true, "is_rm": false, "is_self_dual": true, "is_self_twist": false, "is_twist_minimal": false, "label": "448.8.a.h", "level": 448, "level_is_powerful": false, "level_is_prime": false, "level_is_prime_power": false, "level_is_prime_square": false, "level_is_square": false, "level_is_squarefree": false, "level_primes": [2, 7], "level_radical": 14, "minimal_twist": "56.8.a.b", "nf_label": "1.1.1.1", "prim_orbit_index": 1, "qexp_display": "q+46q^{3}+160q^{5}+7^{3}q^{7}-71q^{9}+\\cdots", "related_objects": [], "relative_dim": 1, "rm_discs": [], "sato_tate_group": "7.2.3.c1", "self_twist_discs": [], "self_twist_type": 0, "space_label": "448.8.a", "trace_display": [0, 46, 160, 343], "trace_hash": 988766973849659317, "trace_moments": [{"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "0.998", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "1.990", "prec": 17}, {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, {"__RealLiteral__": 0, "data": "4.944", "prec": 17}], "trace_zratio": {"__RealLiteral__": 0, "data": "0.000", "prec": 17}, "traces": [0, 1, 0, 46, 0, 160, 0, 343, 0, -71, 0, -6840, 0, 2900, 0, 7360, 0, 16566, 0, -6718, 0, 15778, 0, 976, 0, -52525, 0, -103868, 0, 61662, 0, 69236, 0, -314640, 0, 54880, 0, 533062, 0, 133400, 0, 183158, 0, 966864, 0, -11360, 0, 190268, 0, 117649, 0, 762036, 0, 785010, 0, -1094400, 0, -309028, 0, 2893594, 0, 95896, 0, -24353, 0, 464000, 0, -991644, 0, 44896, 0, -1068160, 0, 2523458, 0, -2416150, 0, -2346120, 0, -285848, 0, -4622651, 0, 7094938, 0, 2650560, 0, 2836452, 0, -252390, 0, 994700, 0, 3184856, 0, -1074880, 0, -1824794, 0, 485640, 0, 9618848, 0, 16775316, 0, 2524480, 0, -2724284, 0, -5398250, 0, 24520852, 0, -25129562, 0, 156160, 0, -205900, 0, 5682138, 0, 27298429, 0, 8425268, 0, -20904000, 0, -9641456, 0, 44475744, 0, -22016046, 0, -2304274, 0, -16618880, 0, 51643714, 0, -55526818, 0, 8752328, 0, -19836000, 0, 9865920, 0, 5411854, 0, -20437782, 0, -70022296, 0, -1176186, 0, 11077760, 0, 80519860, 0, 36110460, 0, 334768, 0, -14998072, 0, -50342400, 0, -37176964, 0, -54338517, 0, 476978, 0, 107405116, 0, -18016075, 0, 133105324, 0, 113389884, 0, 132257532, 0, 4411216, 0, 85289920, 0, -113311440, 0, -35626724, 0, 3877528, 0, -147799314, 0, 21344000, 0, 195010826, 0, -66803844, 0, -45615624, 0, 21150066, 0, 29305280, 0, -69296, 0, 45951120, 0, -167507580, 0, -49135360, 0, 154698240, 0, 23747948, 0, 116079068, 0, 48041400, 0, 79848632, 0, 3729275, 0, 12868338, 0, 286473684, 0, -107921520, 0, 98531658, 0, 30442880, 0, -13149008, 0, -257316216, 0, 257738918, 0, 14517370, 0, 18823840, 0, -19482200, 0, 326367148, 0, 304338206, 0, -6675840, 0, 121925760, 0, -213793294, 0, 182840266, 0, -4378002, 0, -77525920, 0, 125601600, 0, -11609940, 0, -503407684, 0, 443691728, 0, 45756200, 0, 359271000, 0, 81266626, 0, -4915756, 0, 455683434, 0, -431324310, 0, -49444480, 0, 62823194, 0, -135906317, 0, -83940524, 0, 835265416, 0, 462975040, 0, 710457120, 0, 2830400, 0, 331634352, 0, 442467008, 0, 15343360, 0, -128957854, 0, 771664536, 0, 549014904, 0, 347991942, 0, -3896480, 0, -773188702, 0, -421768080, 0, -125317064, 0, -111290388, 0, -152322500, 0, -248319500, 0, 65261924, 0, -755430032, 0, -37847402, 0, -158663040, 0, 369427758, 0, -1155959852, 0, -473574240, 0, 40353607, 0, 7183360, 0, 383442832, 0, 676699948, 0, -301217200, 0, -884640430, 0, -170905600, 0, 261378348, 0, -273898680, 0, -848740215, 0, 1255727734, 0, 403753280, 0, 718777624, 0, -13004218, 0, 269258430, 0, 557666762, 0, -961584000, 0, 178819800, 0, 350444120, 0, -443506976, 0, -2097675956, 0, -375379200, 0, -68647344, 0, 370722550, 0, 16168416, 0, -1012738116, 0, -45735680, 0, -2158866244, 0, -105996604, 0, 199648270, 0, 200784400, 0, -739624160, 0, -3646144080, 0, 1950022174, 0, 2375610844, 0, 992502742, 0, 1135190080, 0, -2554233628, 0, -645883146, 0, -265901982, 0, -13509028, 0, -870129150, 0, 32892328, 0, -912456000, 0, 1874486760, 0, 1267946062, 0, 453832320, 0, -6556768, 0, 2614086264, 0, -8353079, 0, -2214424372, 0, -40382400, 0, -940137972, 0, -1797374126, 0, -1252800720, 0, -3221025616, 0, 159152000, 0, -1143516986, 0, -1720677288, 0, 330188580, 0, -3571890992, 0, 509576960, 0, -2079362758, 0, -340133892, 0, 3703913560, 0, -6613349760, 0, 352862950, 0, -55735710, 0, 2368319604, 0, 1545879800, 0, 15399328, 0, -291967040, 0, -1505478304, 0, -689911312, 0, 3419908044, 0, 1021492692, 0, 77702400, 0, -366378880, 0, -1706426204, 0, -1710140344, 0, -2402570784, 0, 1539015680, 0, -2499571782, 0, 476642796, 0, 865546094, 0, 697785224, 0, 2684050560, 0, -1301433120, 0, 4940635336, 0, 3351418902, 0, 3050606658, 0, -828739450, 0, 1146963576, 0, -3403872871, 0, -205445174, 0, 531158200, 0, -435885440, 0, 5215934664, 0, -804719160, 0, -3712906942, 0, 6083846472, 0, -863720000, 0, 1337843584, 0, -6808616, 0, -414245316, 0, -98045864, 0, 3923336320, 0, -6967156158, 0, 2803905600, 0, -5212326240, 0, 2246472462, 0, -4020729920, 0, -1585569293, 0, -3522364938, 0, 3332824744, 0, 178366288, 0, -51264400, 0, 7439897826, 0, -6798768444, 0, 2433563734, 0, -5369468400, 0, -32944000, 0, 2941106310, 0, -465127448, 0, 8970497996, 0, -5804811174, 0, 909142080, 0, -3072976824, 0, -7637049000, 0, 943486970, 0, 70406724, 0, 4367748640, 0, -7515671296, 0, 972903036, 0, 551777200, 0, -8822486330, 0, 1348042880, 0, -402928938, 0, -3231781926, 0, -101375168, 0, -86569770, 0, 758875625, 0, 2113751520, 0, 8830705092, 0, -3341620912, 0, -7705348680, 0, -1542632960, 0, 341182100, 0, 75839360, 0, -1711538002, 0, -6408997922, 0, 7116119040, 0, -9494489668, 0, -19792182960, 0, 1092405608, 0, 9512266566, 0, -3522567360, 0, -179165518, 0, -9056165280, 0, -2082271640, 0, 2209904400, 0, -368683840, 0, 60182112, 0, 3673037072, 0, -655928640, 0, 10340021690, 0, 5455666700, 0, 5873332988, 0, -625904342, 0, 591943548, 0, -3394047604, 0, 8262994240, 0, 13177789464, 0, 2276529000, 0, -10555285806, 0, 166574520, 0, -8884290880, 0, 3034195428, 0, 4532456268, 0, -658559450, 0, -3581110516, 0, 1400372480, 0, 3299264864, 0, -11425691850, 0, 20295208, 0, 67574336, 0, -3173760000, 0, -11836545936, 0, 762102916, 0, 5753933388, 0, 11855990228, 0, -3238796550, 0, -10396837820, 0, 10777536757, 0, 16017069024, 0, 18930586504, 0, 865896640, 0, 6782844960, 0, -1987445816, 0, -896181200, 0, 8470190648, 0, -3270045120, 0, -503740598, 0, -934429412, 0, 17028280008, 0, 13999557476, 0, -11203567360, 0, -8182361690, 0, -307088640, 0, 289321278, 0, -1851599750, 0, -188189760, 0, 8391422600, 0, 20924166046, 0, -9834491524, 0, 12113860808, 0, -3636620900, 0, 8410652236, 0, -1230455444, 0, 7306214400, 0, -6404708616, 0, 12883177600, 0, 556243274, 0, -3566192320, 0, -8619439766, 0, 278098400, 0, 5777673600, 0, -4667067972, 0, 3151979688, 0, 17919690, 0, -17260452720, 0, 53562880, 0, -23156753464, 0, 6083203094, 0, -8275844830, 0, 20409819488, 0, -2399691520, 0, -6495392352, 0, -70623700, 0, 3652295154, 0, 16509931816, 0, 16526466000, 0, 17612653012, 0, 13847510920, 0, 3738264796, 0, 1948973334, 0, -5948314240, 0, -7191404848, 0, 24002656836, 0, -13447674065, 0, 20961437964, 0, -8694162720, 0, 9363361147, 0, -19840918260, 0, 520268512, 0, 3922695076, 0, 76316480, 0, 8870291102, 0, 2651798494, 0, 2889866924, 0, -1975075384, 0, 17184818560, 0, -6251690582, 0, 1955200320, 0, -2875767600, 0, 129560374, 0, -7170072000, 0, 15975704846, 0, 38422209136, 0, -19343322870, 0, -27800975300, 0, 21296851840, 0, -24082632972, 0, -3307019408, 0, 31618932840, 0, -1278220424, 0, 18142381440, 0, 130198400, 0, 4269230232, 0, 13004475660, 0, 15255180192, 0, 21161205120, 0, 31656443204, 0, -682938208, 0, -5153759472, 0, -48529375920, 0, 705794560, 0, -7551503778, 0, 23905075240, 0, -5932061284, 0, -3097664000, 0, -27999081550, 0, -1191047436, 0, 43631908662, 0, -790365982, 0, 25254685584, 0, -18129830400, 0, 4675541986, 0, 16007629332, 0, 9723495352, 0, 178762208, 0, -5700275840, 0, -17288824560, 0, 7318028200, 0, -35566680292, 0, 23144796250, 0, 620404480, 0, -19401331680, 0, 17713793902, 0, -22718990415, 0, 193424164, 0, -23647890240, 0, -46263523632, 0, -5119357848, 0, 17964229114, 0, -19045698574, 0, -7006835000, 0, 7070403002, 0, 1726347600, 0, 383275750, 0, -39105823244, 0, 31201732160, 0, 3002048504, 0, 943659264, 0, -21391497312, 0, -34749781472, 0, -10688615040, 0, 42678642296, 0, -55368083816, 0, -6803748000, 0, 47935278204, 0, -7298499840, 0, -5273697180, 0, -27852152610, 0, 16993676868, 0, 18378631572, 0, 3384010560, 0, 1784198902, 0, -46426020100, 0, -18429672492, 0, -21784415040, 0, -9620373950, 0, -828959200, 0, 1856265922, 0, 47296693280, 0, -39968294934, 0, -11087360, 0, 1588613136, 0, 28912582388, 0, 17638370272, 0, -7010159226, 0, 7352179200, 0, 31128197608, 0, 40421813378, 0, -20641909660, 0, -13405687900, 0, -26801212800, 0, -24017647528, 0, -40693459780, 0, 25073457318, 0, 3637344816, 0, -7861657600, 0, 12481590960, 0, -34643013864, 0, -403431798, 0, 32869669044, 0, -50784531600, 0, -12599339280, 0, 20575320200, 0, 185701568, 0, -39042049890, 0, 3799671680, 0, 16093786168, 0, -1938188459, 0, -17132162898, 0, -79453742338, 0, 18572650880, 0, -10159476646, 0, 27618311980, 0, 33063770704, 0, 76390901488, 0, 7686624000, 0, -19024255144, 0, -35236833364, 0, -65792920320, 0, 12385887780, 0, 12775781120, 0, 53733001322, 0, 25652671052, 0, -19439164492, 0, -26578761198, 0, 1484184000, 0, 114825424, 0, -63790652830, 0, 8225710800, 0, -114743161440, 0, 2058934080, 0, 16120429520, 0, -16427574504, 0, -5144338696, 0, 684543376, 0, 45835789440, 0, 36907080632, 0, -96493093976, 0, 43891499228, 0, -53799951358, 0, -17267443200, 0, -731931000, 0, -644229328, 0, -100426229952, 0, -54606614148, 0, 15765065280, 0, 17053237300, 0, -12751698652, 0, -32407990052, 0, 743747136, 0, -9993826700, 0, 18634102560, 0, 1563139266, 0, 40075149620, 0, -18638111331, 0, -2103841280, 0, 32510938300, 0, 11293888596, 0, -99307847224, 0, -40337110590, 0, -41170594560, 0, 163603454, 0, 36924030000, 0, 52274577646, 0, 9183820420, 0, 41238226880, 0, -17695138560, 0, 9236082400, 0, 36839954788, 0, -93574661826, 0, 2322779200, 0, -55977225094, 0, 766169760, 0, -167722627680, 0, -86904341096, 0, -6179513725, 0, 89701020004, 0, 47626178314, 0, -59949048340, 0, -3666703694, 0, -3117152000, 0, -71000493624, 0, 45655126132, 0, 41803605228, 0, 171886204080, 0, 52218743680, 0, 59618767968, 0, -35057505158, 0, 3942404078, 0, 38892730212, 0, 48694112960, 0, -29710624716, 0, 31684028818, 0, -5291902600, 0, -12231491172, 0, -1068134400, 0, 45364333476, 0, -19762756624, 0, 12681127288, 0, 6661864392, 0, -40025940900, 0, -120384022392, 0, 73967774748, 0, 1513047088, 0, 111076485144, 0, -34206927040, 0, 1408356000, 0, -25690666546, 0, 576626102, 0, 86226390960, 0, 29254442560, 0, -23046458306, 0, 58325518852, 0, 107945184688, 0, -77014884248, 0, -700480320, 0, -105011346902, 0, -38865823920, 0, -301611328, 0, 27894659200, 0, -12404147200, 0, 120247968144, 0, 109839578360, 0, -16712367474, 0, -12219966332, 0, -41232650250, 0, -47360693776, 0, -101863521112, 0, -53429004720, 0, 66941795904, 0, -1857590400, 0, 1329992104, 0, 48648416400, 0, 1451082522, 0, -4735357968, 0, -80545229440, 0, -82679209796, 0, 7175898880, 0, -50695164702, 0, -57628833120, 0, 70990676480, 0, 2824147744, 0, 4971583016, 0, -18614738242, 0, 11732305416, 0, 7320992000, 0, 75887095128, 0, 189223218711, 0, -52601781356, 0, 132070326614, 0, 142983360000, 0, -76578836466, 0, 66888713318, 0, 29209595710, 0, 15188674680, 0, 13002660160, 0, -16952590844, 0, -164306985632, 0, -7900423600, 0, -22913718492, 0, -786520960, 0, 65947559040, 0, -70883100056, 0, -95650686868, 0, 93594496, 0, 72909349440, 0, -15646159032, 0, 195233280466, 0, 117534742908, 0, -5716910060, 0, -69011889600, 0, -15654925000, 0, -304214088960, 0, 7254472638, 0, -114280636504, 0, 16231695700, 0, -205532846814, 0, 14153974190, 0, -81537418680, 0, 5245815722, 0, 10051711040, 0, 108942701784, 0, 51031646504, 0, 150589754640, 0, 71110470800, 0, -21745010720, 0, -135107215296, 0, -23768528, 0, 64335963192, 0, 150159326310, 0, -13430483840, 0, 13173395248, 0, 117016334230, 0, -69252001984, 0, 15761234160, 0, 133642466560, 0, 1064863112, 0, -72875729800, 0, -125300379216, 0, 157315770024, 0, -151986024850, 0, -57455099940, 0, 46988663832, 0, -164098183062, 0, 112010150098, 0, 113673139200, 0, 13437015744, 0, 50265507638, 0, -16853428480, 0, -164934730566, 0, 452864000, 0, -78495605384, 0, -7047235028, 0, 1920326864, 0, 2639564444, 0, 53061496320, 0, -353243003760, 0, -110518256064, 0, 55564535488, 0, -4181092740, 0, 70794721280, 0, 97634569796, 0, 8145546164, 0, 3858034707, 0, 55105751088, 0, -5036937400, 0, 21925568616, 0, 379803435120, 0, -269483965598, 0, 39815120324, 0, -20633256640, 0, 48405286620, 0, 31054969418, 0, -967844544, 0, 248751737152, 0, 123466325760, 0, 16478200200, 0, -244235019254, 0, -59865923520, 0, 28286848746, 0, 87842384640, 0, -7625763236, 0, -102541259172, 0, 27388080776, 0, 154165269492, 0, 55678710720, 0, -84688114672, 0, 140327906268, 0, 197586209442, 0, 79165444100, 0, 1279141325, 0, -47663793484, 0, 75074938688, 0, 52760324496, 0, -200468685776, 0, -123710192320, 0, -156578152066, 0, 4413839934, 0, 515398457568, 0, -300551821592, 0, -67482892800, 0, -100019782430, 0, 24433277200, 0, 245304834690, 0, 98260473612, 0, -20050730240, 0, 76093824912, 0, 146205060954, 0, -8050681764, 0, 298437076712, 0, -17806462080, 0, -37017081360, 0, 78485918508, 0, -180079972482, 0, -170793719332, 0, -60621600000, 0, -244406814874, 0, -9390284772, 0, 33796358694, 0, -1042524160, 0, -39731120000, 0, 76730279072, 0, 139794428880, 0, 61540804864, 0, 54350952360, 0, 10441907840, 0, -9960525728, 0, -30229537404, 0, -27960222400, 0, -19055284536, 0, -120868805120, 0, -252118445074, 0, -4510109744, 0, 478952504640, 0, 262165485464, 0, -6055584320, 0, -145636987320, 0, 249848066784, 0, -320489183268, 0, -88259462088, 0, 52086101100, 0, 128979657600, 0, 2462895008, 0, -161207420917, 0, 8045112240, 0, 59108441280, 0, 88404448874, 0, 103337733252, 0, 1695556020, 0, 273115437544, 0, -184953576320, 0, 161588431910, 0, 70467069542, 0, 4979457910, 0, -63846533400, 0, -75771878400, 0, -162028787148, 0, 226001195090, 0, 178424793228, 0, 153309938224, 0, 6456577120, 0, 159345835968, 0, -275304488, 0, 13706256090, 0, 226181467028, 0, -2358162400, 0, -550755842400, 0, -6682394600, 0, 342235299996, 0, 132531846830, 0, 61350853120, 0, 10493751294, 0, 101424640616, 0, -316576318500, 0, 111943931764, 0, 108271991680, 0, 275657017424, 0, -246995546400, 0, 277899884856, 0, -164343531758, 0, -48194752000, 0, 104388004658, 0, -20391867936, 0, 135290890260, 0, 177088876512, 0, -141542468800, 0, -21395862608, 0, 5913139152, 0, -2289813120, 0, -13845768646, 0, 56105104000, 0, 11934040274, 0, -267021314004, 0, 149766770600, 0, -124042241968, 0, 41820535680, 0, 48630486800, 0, -439375880078, 0, 4743072924, 0, 102586812480, 0, -43823788800, 0, -351304254000, 0, -73331099842, 0, -310138424754, 0, 43400400620, 0, -135798434400, 0, -161027772200, 0, 103000078992, 0, 172023746698, 0, 62714211238, 0, 200916437440, 0, -278987648, 0, -45130488744, 0, -345720879616, 0, 173106852952, 0, -132544631450, 0, -1501654686, 0, 200340874184, 0, 497401680872, 0, 25381751200, 0, 115004419840, 0, 254290433760, 0, -405834371180, 0, -26591390560, 0, 12258966092, 0, -2080674880, 0, -1296542268, 0, 663007383389, 0, -18534731148, 0, -89427409500, 0, 43081348800, 0, -148661968596, 0, 371675456280, 0, 376930725720, 0, -4511707376, 0, 89226681920, 0, -172074281614, 0, -3982209420, 0, -47397512464, 0, -174145103582, 0, 34908278750, 0, 137039744010, 0, 420538218148, 0, -3262529520, 0, -172668835612, 0, 28611168000, 0, 406212434232, 0, 116381358450, 0, 6639455456, 0, -153714561952, 0, 56071059200, 0, 152186262704, 0, 11893038180, 0, -308645329990, 0, -734650993440, 0, -70961116160, 0, 575735320202, 0, 6924659488, 0, 15694376600, 0, -109561366362, 0, -335628152960, 0, 110947642880, 0, -64619420864, 0, -416296324092, 0, -78730748092, 0, 123229953000, 0, 34849106344, 0, -294813904412, 0, 43071094178, 0, -415416756118, 0, -10983575040, 0, -59269567800, 0, 27874452718, 0, -436746524728, 0, -61146752328, 0, 59315608000, 0, -910440416160, 0, -307643771748, 0, -244965183008, 0, -1686104308, 0, 2586946560, 0, -112696572888, 0, 437564262036, 0, 418459000620, 0, -203064658400, 0, -162038098560, 0, 156299417862, 0, -775586806560, 0, -262106535544, 0, 217967060396, 0, 15014166200, 0, -416583602880, 0, -163790983026, 0, -147944238330, 0, -95784495440, 0, -345418599040, 0, -466923481442, 0, -3410939400, 0, -904641518880, 0, -369889183266, 0, -16959456640, 0, -50473912538, 0, 56096879360, 0, 2768377152, 0, -140548651320, 0, 31943723200, 0, -5669252872, 0, 21548355542, 0, -105501756704, 0, -30172717440, 0, 32125504000, 0, 293918960026, 0, 475640997740, 0, 183963279552, 0, -46615866731, 0, 242804743775, 0, -619374160032, 0, -581675423360, 0, 270173317448, 0, 18301739912, 0, -583383052800, 0, -28791599732, 0, 486634527888, 0, 233507594000, 0, -913651998, 0, 312003547840, 0, -246332640, 0, -156126189784, 0, 286496037688, 0, -462320888014, 0, 380097735040, 0, 452225774814, 0, -65864881920, 0, -20339631564, 0, -50482088760, 0, 158800438720, 0, 104720334000, 0, 22191082566, 0, 36265443500, 0, -485543147076, 0, -372661618450, 0, -68657463984, 0, 243686792160, 0, -545493267382, 0, 563657561688, 0, -408677380480, 0, -729143616448, 0, -437585519590, 0, 139572989688, 0, 970827200, 0, -103341303360, 0, -6995747718, 0, -417031552338, 0, -26522291520, 0, -30293734700, 0, -42544317120, 0, 113750582736, 0, -164731083736, 0, 322546701696, 0, 183515153754, 0, -2161444480, 0, 155601467196, 0, -43494408800, 0, 151766183744, 0, 1010947307760, 0, -346295664000, 0, -525581825100, 0, -81687337406, 0, 571280349958, 0, 29690460064, 0, 5262772480, 0, -56148992126, 0, 3108419456, 0, 110181212584, 0, -561008131720, 0, -145992960000, 0, 168820397516, 0, -44232543922, 0, 18269451336, 0, 557337565830, 0, 299917881600, 0, 35056734136, 0, -159720360096, 0, -395456216882, 0, 264680935848, 0, 202871369920, 0, -1333874049840, 0, -18299463178, 0, -107813195600, 0, 143780861580, 0, -148984641300, 0, 188312112072, 0, -19086822272, 0, -478254539720, 0, 1542465004828, 0, -1049082880, 0, 464017202632, 0, 456938292960, 0, 119361236106, 0, 736785175104, 0, 418253802240, 0, -339552398600, 0, 870806979184, 0, -73955125760, 0, -669771013262, 0, -1336492640, 0, -864316600816, 0, -470421208639, 0, 312010868160, 0, 409455259230, 0, -354307899520, 0, -91422507536, 0, -265203724786, 0, 17183999442, 0, 1383236200, 0, 13256784750, 0, -364717818036, 0, 389628769808, 0, -1780998944, 0, -144666451440, 0, -150422075520, 0, 110478359238, 0, -119855138580, 0, -736937020184, 0, 405647441510, 0, -287579860160, 0, -42983752952, 0, 311474836400, 0, 449466772052, 0, 783300880368, 0, -200448115200, 0, 51118513552, 0, -21608012626, 0, -38172603084, 0, 174714138088, 0, -515364098560, 0, -358294544174, 0, 7016904374, 0, -376388637740, 0, -731377644398, 0, -52246617500, 0, 473984640, 0, 758997908640, 0, -1044504640566, 0, 13308778788, 0, -182962717760, 0, 430023179420, 0, -85173588500, 0, -17625959376, 0, -452126906774, 0, -275308366080, 0, -153937980858, 0, -183390846022, 0, 386005439600, 0, 22384839932, 0, 52830172800, 0, 962511638116, 0, 903607565436, 0, 32565806880, 0, 15179323874, 0, -571502558720, 0, -259112500976, 0, 557237597168, 0, 1145751847200, 0, 9387995648, 0, -167284561400, 0, 328830663600, 0, 855529766124, 0, -12981658886, 0, -378964178410, 0, -332698041280, 0, -56600950424, 0, -111791334768, 0, 467551879996, 0, 336085862400, 0, -54421422720, 0, 367745382808, 0, -285041905962, 0, 376834635000, 0, 383546842800, 0, 592626169600, 0, 211392813240, 0, 126713720994, 0, 25587190604, 0, -919857266988, 0, -1058135961600, 0, 5504340320, 0, 16372708416, 0, -550901367746, 0, -396494229236, 0, 140433072000, 0, 634622883114, 0, 12792526400, 0, 482345078058, 0, 809811909900, 0, -8917713600, 0, -162435964320, 0, 966359042762, 0, -214685126712, 0, 415294556274, 0, 378931136640, 0, 144991065648, 0, 361740762036, 0, 13841287201, 0, 26215244520, 0, 247340768000, 0, 437488066956, 0, -793980825120, 0, -869590854710, 0, 64771301408, 0, 2463892480, 0, 443096143794, 0, 529984889852, 0, 35741945564, 0, 524633148928, 0, 95847304850, 0, 279827342324, 0, 131520891376, 0, -328603176000, 0, -380688862180, 0, -240876528640, 0, -1201775189766, 0, -31502112688, 0, 556725445218, 0, 232108082164, 0, -110385809920, 0, 111330963888, 0, -19790972128, 0, -298788048192, 0, -546164642880, 0, 547185287040, 0, -103317499600, 0, 818318475412, 0, -2658901184, 0, 168005577084, 0, 163438830720, 0, -239647258622, 0, 759456863536, 0, -303431667490, 0, 479433675910, 0, -25508241000, 0, -409032525604, 0, -528607733928, 0, 810182038552, 0, 11244831200, 0, -58620620800, 0, 636985502320, 0, 147903797028, 0, 149362282680, 0, -5769930446, 0, -273028192640, 0, -88019431920, 0, 89652773364, 0, 17564119568, 0, 62954679488, 0, -273622455040, 0, -5268692000, 0, -428618010600, 0, -320053864636, 0, -93947247240, 0, -384411325440, 0, 1104122214456, 0, -1959479998560, 0, 22108670550, 0, -618593006990, 0, -505229991200, 0, -291117893745, 0, -32353523814, 0, -1098828647508, 0, -338572296612, 0, -399931485120, 0, 2797711869216, 0, 1109928056078, 0, 430714612762, 0, -183976538032, 0, 76262847360, 0, 30624026010, 0, 265787683066, 0, -565504915352, 0, 23932351552, 0, 138487375040, 0, 533478332482, 0, 180443973496, 0, 565531395400, 0, -673956540720, 0, 111645635840, 0, -1159989355536, 0, 246540725032, 0, 408033390692, 0, 491225127368, 0, -881123472900, 0, 121982730724, 0, -1198933744366, 0, -15562872180, 0, -4460446774, 0, -208229299200, 0, -193731147600, 0, -90853467664, 0, -612931456424, 0, 405675523098, 0, 790501653760, 0, 92355641490, 0, -24526452512, 0, 9649348507, 0, -346942470652, 0, 536227024320, 0, 89939214720, 0, 534332447174, 0, 191279699366, 0, -132285309600, 0, 488097065280, 0, -1220192013122, 0, 189537703192, 0, 975773033580, 0, 92718390144, 0, -329823312000, 0, -569395505920, 0, 1760042917440, 0, 734882422916, 0, 661897853526, 0, 183514172160, 0, -59303844536, 0, 61335191400, 0, 373029163324, 0, -889792852020, 0, -544619659360, 0, 69262928072, 0, -1278844863800, 0, -1762934199120, 0, 120202333160, 0, -32871227840, 0, 967784397906, 0, 1048917954270, 0, -1107801116712, 0, 1285619356712, 0, 84985312000, 0, -152122892768, 0, 1333892000760, 0, 104795671400, 0, -99298810800, 0, 143093017100, 0, -956349728992, 0, -58798139504, 0, -719502852908, 0, -1495402442932, 0, 834549546240, 0, -137246180292, 0, 346666005694, 0, -200958400, 0, 387851214480, 0, -128755065600, 0, 196384590672, 0, 1416379084404, 0, 1345159568396, 0, 598205880360, 0, -594065110720, 0, 1631248619014, 0, -23546038992, 0, 1102446284152, 0, -686995455758, 0, 973415435520, 0, 133258248000, 0, 1858297476676, 0, 1456196387384, 0, 127157834650, 0, 283543081250, 0, -999090504064, 0, 651636403878, 0, 1216756668308, 0, -237072935712, 0, 214054973440, 0, 5545766688, 0, -2232351292320, 0, 1334871071334, 0, -485771982000, 0, -1089378560, 0, -181627531752, 0, 1697580210440, 0, -347369173788, 0, 27236128242, 0, -66279250560, 0, 1099633461040, 0, -17474474040, 0, -2081673329040, 0, 9156007634, 0, -15687338240, 0, -1163559320624, 0, -142492544000, 0, -248458060752, 0, 550558343192, 0, -1287957751300, 0, 299997615582, 0, -740491121692, 0, -1742418522288, 0, 26643266704, 0, -1114744985280, 0, 2007067798452, 0, -2239997462060, 0, -1510861697260, 0, -36356835172, 0, 448624896000, 0, 1193425560426, 0, -38980058184, 0, -103050943202, 0, -930374431034, 0, -833972198400, 0, 68479356610, 0, -558470439737, 0, 215074931356, 0, -112520447628, 0, 359435593920, 0, -24707427882, 0, 1532321781390, 0, 68869049200, 0, 447280786192, 0, 1319930244050, 0, 1462346130960, 0, 8223061568, 0, 137301019476, 0, 1641571070842, 0, -253691086880, 0, 367577741598, 0, -615873585624, 0, -795285929760, 0, 691521572872, 0, -563578390080, 0, 336629297200, 0, -1250627419440, 0, -1080291539948, 0, 54896397842, 0, 533251959040, 0, -47289392006, 0, 1064660627500, 0, -1456586790204, 0, 668857605682, 0, 28538606080, 0, 18245940128, 0, 470409784528, 0, 29945533680, 0, -900171872622, 0, -20402304000, 0, 814834519492, 0, -1983160849368, 0, -958784884416, 0, -1045073559090, 0, 1190383652160, 0, 1819676693476, 0, 282965930512, 0, 340428440506, 0, 530277292800, 0, -1087802951040, 0, 1950018218118, 0, 231561032800, 0, -2128122087072, 0, -1709967412992, 0, 389370197440, 0, 7901617548, 0, -891708474266, 0, -195642049280, 0, 826354539244, 0, -859114944000, 0, -1462061434104, 0, -876102134404, 0, -9410061056, 0, -152374706576, 0, 10814897500, 0, 991589021648, 0, 593117405376, 0, 325238538092, 0, -221537919078, 0, 470577009600, 0, 79411989600, 0, -1120315546730, 0, 1779273151656, 0, 560705431000, 0, -74420391680, 0, -91204379826, 0, -1798867869224, 0, 37318180200, 0, -1280869895018, 0, 1435279679360, 0, 394000487616, 0, 3443308558560, 0, -4633596604, 0, -104088425232, 0, -928769787840, 0, 43408326144, 0, -1579377029382, 0, -1852771861290, 0, -984008876352, 0, -298454298450, 0, 830773683600, 0, 53635532272, 0, -3034851419520, 0, -540932419480, 0, -491676291840, 0, 1034399535192, 0, 11282068504, 0, 1963217545616, 0, 462191520364, 0, -1221927840000, 0, -2464159587362, 0, -165598333012, 0], "weight": 8, "weight_parity": 1, "id": null, "artin_degree": null, "artin_field": null, "artin_field_label": null, "artin_image": null, "embedded_related_objects": null, "projective_field": null, "projective_field_label": null, "projective_image": null, "projective_image_type": null, "qexp": [[0], 1, 0, 46, 0, 160, 0, 343, 0, -71, 0, -6840, 0, 2900, 0, 7360, 0, 16566, 0, -6718, 0, 15778, 0, 976, 0, -52525, 0, -103868, 0, 61662, 0, 69236, 0, -314640, 0, 54880, 0, 533062, 0, 133400, 0, 183158, 0, 966864, 0, -11360, 0, 190268, 0, 117649, 0, 762036, 0, 785010, 0, -1094400, 0, -309028, 0, 2893594, 0, 95896, 0, -24353, 0, 464000, 0, -991644, 0, 44896, 0, -1068160, 0, 2523458, 0, -2416150, 0, -2346120, 0, -285848, 0, -4622651, 0, 7094938, 0, 2650560, 0, 2836452, 0, -252390, 0, 994700, 0, 3184856, 0, -1074880, 0, -1824794, 0, 485640, 0, 9618848, 0, 16775316, 0, 2524480, 0, -2724284, 0, -5398250, 0, 24520852, 0, -25129562, 0, 156160, 0, -205900, 0, 5682138, 0, 27298429, 0, 8425268, 0, -20904000, 0, -9641456, 0, 44475744, 0, -22016046, 0, -2304274, 0, -16618880, 0, 51643714, 0, -55526818, 0, 8752328, 0, -19836000, 0, 9865920, 0, 5411854, 0, -20437782, 0, -70022296, 0, -1176186, 0, 11077760, 0, 80519860, 0, 36110460, 0, 334768, 0, -14998072, 0, -50342400, 0, -37176964, 0, -54338517, 0, 476978, 0, 107405116, 0, -18016075, 0, 133105324, 0, 113389884, 0, 132257532, 0, 4411216, 0, 85289920, 0, -113311440, 0, -35626724, 0, 3877528, 0, -147799314, 0, 21344000, 0, 195010826, 0, -66803844, 0, -45615624, 0, 21150066, 0, 29305280, 0, -69296, 0, 45951120, 0, -167507580, 0, -49135360, 0, 154698240, 0, 23747948, 0, 116079068, 0, 48041400, 0, 79848632, 0, 3729275, 0, 12868338, 0, 286473684, 0, -107921520, 0, 98531658, 0, 30442880, 0, -13149008, 0, -257316216, 0, 257738918, 0, 14517370, 0, 18823840, 0, -19482200, 0, 326367148, 0, 304338206, 0, -6675840, 0, 121925760, 0, -213793294, 0, 182840266, 0, -4378002, 0, -77525920, 0, 125601600, 0, -11609940, 0, -503407684, 0, 443691728, 0, 45756200, 0, 359271000, 0, 81266626, 0, -4915756, 0, 455683434, 0, -431324310, 0, -49444480, 0, 62823194, 0, -135906317, 0, -83940524, 0, 835265416, 0, 462975040, 0, 710457120, 0, 2830400, 0, 331634352, 0, 442467008, 0, 15343360, 0, -128957854, 0, 771664536, 0, 549014904, 0, 347991942, 0, -3896480, 0, -773188702, 0, -421768080, 0, -125317064, 0, -111290388, 0, -152322500, 0, -248319500, 0, 65261924, 0, -755430032, 0, -37847402, 0, -158663040, 0, 369427758, 0, -1155959852, 0, -473574240, 0, 40353607, 0, 7183360, 0, 383442832, 0, 676699948, 0, -301217200, 0, -884640430, 0, -170905600, 0, 261378348, 0, -273898680, 0, -848740215, 0, 1255727734, 0, 403753280, 0, 718777624, 0, -13004218, 0, 269258430, 0, 557666762, 0, -961584000, 0, 178819800, 0, 350444120, 0, -443506976, 0, -2097675956, 0, -375379200, 0, -68647344, 0, 370722550, 0, 16168416, 0, -1012738116, 0, -45735680, 0, -2158866244, 0, -105996604, 0, 199648270, 0, 200784400, 0, -739624160, 0, -3646144080, 0, 1950022174, 0, 2375610844, 0, 992502742, 0, 1135190080, 0, -2554233628, 0, -645883146, 0, -265901982, 0, -13509028, 0, -870129150, 0, 32892328, 0, -912456000, 0, 1874486760, 0, 1267946062, 0, 453832320, 0, -6556768, 0, 2614086264, 0, -8353079, 0, -2214424372, 0, -40382400, 0, -940137972, 0, -1797374126, 0, -1252800720, 0, -3221025616, 0, 159152000, 0, -1143516986, 0, -1720677288, 0, 330188580, 0, -3571890992, 0, 509576960, 0, -2079362758, 0, -340133892, 0, 3703913560, 0, -6613349760, 0, 352862950, 0, -55735710, 0, 2368319604, 0, 1545879800, 0, 15399328, 0, -291967040, 0, -1505478304, 0, -689911312, 0, 3419908044, 0, 1021492692, 0, 77702400, 0, -366378880, 0, -1706426204, 0, -1710140344, 0, -2402570784, 0, 1539015680, 0, -2499571782, 0, 476642796, 0, 865546094, 0, 697785224, 0, 2684050560, 0, -1301433120, 0, 4940635336, 0, 3351418902, 0, 3050606658, 0, -828739450, 0, 1146963576, 0, -3403872871, 0, -205445174, 0, 531158200, 0, -435885440, 0, 5215934664, 0, -804719160, 0, -3712906942, 0, 6083846472, 0, -863720000, 0, 1337843584, 0, -6808616, 0, -414245316, 0, -98045864, 0, 3923336320, 0, -6967156158, 0, 2803905600, 0, -5212326240, 0, 2246472462, 0, -4020729920, 0, -1585569293, 0, -3522364938, 0, 3332824744, 0, 178366288, 0, -51264400, 0, 7439897826, 0, -6798768444, 0, 2433563734, 0, -5369468400, 0, -32944000, 0, 2941106310, 0, -465127448, 0, 8970497996, 0, -5804811174, 0, 909142080, 0, -3072976824, 0, -7637049000, 0, 943486970, 0, 70406724, 0, 4367748640, 0, -7515671296, 0, 972903036, 0, 551777200, 0, -8822486330, 0, 1348042880, 0, -402928938, 0, -3231781926, 0, -101375168, 0, -86569770, 0, 758875625, 0, 2113751520, 0, 8830705092, 0, -3341620912, 0, -7705348680, 0, -1542632960, 0, 341182100, 0, 75839360, 0, -1711538002, 0, -6408997922, 0, 7116119040, 0, -9494489668, 0, -19792182960, 0, 1092405608, 0, 9512266566, 0, -3522567360, 0, -179165518, 0, -9056165280, 0, -2082271640, 0, 2209904400, 0, -368683840, 0, 60182112, 0, 3673037072, 0, -655928640, 0, 10340021690, 0, 5455666700, 0, 5873332988, 0, -625904342, 0, 591943548, 0, -3394047604, 0, 8262994240, 0, 13177789464, 0, 2276529000, 0, -10555285806, 0, 166574520, 0, -8884290880, 0, 3034195428, 0, 4532456268, 0, -658559450, 0, -3581110516, 0, 1400372480, 0, 3299264864, 0, -11425691850, 0, 20295208, 0, 67574336, 0, -3173760000, 0, -11836545936, 0, 762102916, 0, 5753933388, 0, 11855990228, 0, -3238796550, 0, -10396837820, 0, 10777536757, 0, 16017069024, 0, 18930586504, 0, 865896640, 0, 6782844960, 0, -1987445816, 0, -896181200, 0, 8470190648, 0, -3270045120, 0, -503740598, 0, -934429412, 0, 17028280008, 0, 13999557476, 0, -11203567360, 0, -8182361690, 0, -307088640, 0, 289321278, 0, -1851599750, 0, -188189760, 0, 8391422600, 0, 20924166046, 0, -9834491524, 0, 12113860808, 0, -3636620900, 0, 8410652236, 0, -1230455444, 0, 7306214400, 0, -6404708616, 0, 12883177600, 0, 556243274, 0, -3566192320, 0, -8619439766, 0, 278098400, 0, 5777673600, 0, -4667067972, 0, 3151979688, 0, 17919690, 0, -17260452720, 0, 53562880, 0, -23156753464, 0, 6083203094, 0, -8275844830, 0, 20409819488, 0, -2399691520, 0, -6495392352, 0, -70623700, 0, 3652295154, 0, 16509931816, 0, 16526466000, 0, 17612653012, 0, 13847510920, 0, 3738264796, 0, 1948973334, 0, -5948314240, 0, -7191404848, 0, 24002656836, 0, -13447674065, 0, 20961437964, 0, -8694162720, 0, 9363361147, 0, -19840918260, 0, 520268512, 0, 3922695076, 0, 76316480, 0, 8870291102, 0, 2651798494, 0, 2889866924, 0, -1975075384, 0, 17184818560, 0, -6251690582, 0, 1955200320, 0, -2875767600, 0, 129560374, 0, -7170072000, 0, 15975704846, 0, 38422209136, 0, -19343322870, 0, -27800975300, 0, 21296851840, 0, -24082632972, 0, -3307019408, 0, 31618932840, 0, -1278220424, 0, 18142381440, 0, 130198400, 0, 4269230232, 0, 13004475660, 0, 15255180192, 0, 21161205120, 0, 31656443204, 0, -682938208, 0, -5153759472, 0, -48529375920, 0, 705794560, 0, -7551503778, 0, 23905075240, 0, -5932061284, 0, -3097664000, 0, -27999081550, 0, -1191047436, 0, 43631908662, 0, -790365982, 0, 25254685584, 0, -18129830400, 0, 4675541986, 0, 16007629332, 0, 9723495352, 0, 178762208, 0, -5700275840, 0, -17288824560, 0, 7318028200, 0, -35566680292, 0, 23144796250, 0, 620404480, 0, -19401331680, 0, 17713793902, 0, -22718990415, 0, 193424164, 0, -23647890240, 0, -46263523632, 0, -5119357848, 0, 17964229114, 0, -19045698574, 0, -7006835000, 0, 7070403002, 0, 1726347600, 0, 383275750, 0, -39105823244, 0, 31201732160, 0, 3002048504, 0, 943659264, 0, -21391497312, 0, -34749781472, 0, -10688615040, 0, 42678642296, 0, -55368083816, 0, -6803748000, 0, 47935278204, 0, -7298499840, 0, -5273697180, 0, -27852152610, 0, 16993676868, 0, 18378631572, 0, 3384010560, 0, 1784198902, 0, -46426020100, 0, -18429672492, 0, -21784415040, 0, -9620373950, 0, -828959200, 0, 1856265922, 0, 47296693280, 0, -39968294934, 0, -11087360, 0, 1588613136, 0, 28912582388, 0, 17638370272, 0, -7010159226, 0, 7352179200, 0, 31128197608, 0, 40421813378, 0, -20641909660, 0, -13405687900, 0, -26801212800, 0, -24017647528, 0, -40693459780, 0, 25073457318, 0, 3637344816, 0, -7861657600, 0, 12481590960, 0, -34643013864, 0, -403431798, 0, 32869669044, 0, -50784531600, 0, -12599339280, 0, 20575320200, 0, 185701568, 0, -39042049890, 0, 3799671680, 0, 16093786168, 0, -1938188459, 0, -17132162898, 0, -79453742338, 0, 18572650880, 0, -10159476646, 0, 27618311980, 0, 33063770704, 0, 76390901488, 0, 7686624000, 0, -19024255144, 0, -35236833364, 0, -65792920320, 0, 12385887780, 0, 12775781120, 0, 53733001322, 0, 25652671052, 0, -19439164492, 0, -26578761198, 0, 1484184000, 0, 114825424, 0, -63790652830, 0, 8225710800, 0, -114743161440, 0, 2058934080, 0, 16120429520, 0, -16427574504, 0, -5144338696, 0, 684543376, 0, 45835789440, 0, 36907080632, 0, -96493093976, 0, 43891499228, 0, -53799951358, 0, -17267443200, 0, -731931000, 0, -644229328, 0, -100426229952, 0, -54606614148, 0, 15765065280, 0, 17053237300, 0, -12751698652, 0, -32407990052, 0, 743747136, 0, -9993826700, 0, 18634102560, 0, 1563139266, 0, 40075149620, 0, -18638111331, 0, -2103841280, 0, 32510938300, 0, 11293888596, 0, -99307847224, 0, -40337110590, 0, -41170594560, 0, 163603454, 0, 36924030000, 0, 52274577646, 0, 9183820420, 0, 41238226880, 0, -17695138560, 0, 9236082400, 0, 36839954788, 0, -93574661826, 0, 2322779200, 0, -55977225094, 0, 766169760, 0, -167722627680, 0, -86904341096, 0, -6179513725, 0, 89701020004, 0, 47626178314, 0, -59949048340, 0, -3666703694, 0, -3117152000, 0, -71000493624, 0, 45655126132, 0, 41803605228, 0, 171886204080, 0, 52218743680, 0, 59618767968, 0, -35057505158, 0, 3942404078, 0, 38892730212, 0, 48694112960, 0, -29710624716, 0, 31684028818, 0, -5291902600, 0, -12231491172, 0, -1068134400, 0, 45364333476, 0, -19762756624, 0, 12681127288, 0, 6661864392, 0, -40025940900, 0, -120384022392, 0, 73967774748, 0, 1513047088, 0, 111076485144, 0, -34206927040, 0, 1408356000, 0, -25690666546, 0, 576626102, 0, 86226390960, 0, 29254442560, 0, -23046458306, 0, 58325518852, 0, 107945184688, 0, -77014884248, 0, -700480320, 0, -105011346902, 0, -38865823920, 0, -301611328, 0, 27894659200, 0, -12404147200, 0, 120247968144, 0, 109839578360, 0, -16712367474, 0, -12219966332, 0, -41232650250, 0, -47360693776, 0, -101863521112, 0, -53429004720, 0, 66941795904, 0, -1857590400, 0, 1329992104, 0, 48648416400, 0, 1451082522, 0, -4735357968, 0, -80545229440, 0, -82679209796, 0, 7175898880, 0, -50695164702, 0, -57628833120, 0, 70990676480, 0, 2824147744, 0, 4971583016, 0, -18614738242, 0, 11732305416, 0, 7320992000, 0, 75887095128, 0, 189223218711, 0, -52601781356, 0, 132070326614, 0, 142983360000, 0, -76578836466, 0, 66888713318, 0, 29209595710, 0, 15188674680, 0, 13002660160, 0, -16952590844, 0, -164306985632, 0, -7900423600, 0, -22913718492, 0, -786520960, 0, 65947559040, 0, -70883100056, 0, -95650686868, 0, 93594496, 0, 72909349440, 0, -15646159032, 0, 195233280466, 0, 117534742908, 0, -5716910060, 0, -69011889600, 0, -15654925000, 0, -304214088960, 0, 7254472638, 0, -114280636504, 0, 16231695700, 0, -205532846814, 0, 14153974190, 0, -81537418680, 0, 5245815722, 0, 10051711040, 0, 108942701784, 0, 51031646504, 0, 150589754640, 0, 71110470800, 0, -21745010720, 0, -135107215296, 0, -23768528, 0, 64335963192, 0, 150159326310, 0, -13430483840, 0, 13173395248, 0, 117016334230, 0, -69252001984, 0, 15761234160, 0, 133642466560, 0, 1064863112, 0, -72875729800, 0, -125300379216, 0, 157315770024, 0, -151986024850, 0, -57455099940, 0, 46988663832, 0, -164098183062, 0, 112010150098, 0, 113673139200, 0, 13437015744, 0, 50265507638, 0, -16853428480, 0, -164934730566, 0, 452864000, 0, -78495605384, 0, -7047235028, 0, 1920326864, 0, 2639564444, 0, 53061496320, 0, -353243003760, 0, -110518256064, 0, 55564535488, 0, -4181092740, 0, 70794721280, 0, 97634569796, 0, 8145546164, 0, 3858034707, 0, 55105751088, 0, -5036937400, 0, 21925568616, 0, 379803435120, 0, -269483965598, 0, 39815120324, 0, -20633256640, 0, 48405286620, 0, 31054969418, 0, -967844544, 0, 248751737152, 0, 123466325760, 0, 16478200200, 0, -244235019254, 0, -59865923520, 0, 28286848746, 0, 87842384640, 0, -7625763236, 0, -102541259172, 0, 27388080776, 0, 154165269492, 0, 55678710720, 0, -84688114672, 0, 140327906268, 0, 197586209442, 0, 79165444100, 0, 1279141325, 0, -47663793484, 0, 75074938688, 0, 52760324496, 0, -200468685776, 0, -123710192320, 0, -156578152066, 0, 4413839934, 0, 515398457568, 0, -300551821592, 0, -67482892800, 0, -100019782430, 0, 24433277200, 0, 245304834690, 0, 98260473612, 0, -20050730240, 0, 76093824912, 0, 146205060954, 0, -8050681764, 0, 298437076712, 0, -17806462080, 0, -37017081360, 0, 78485918508, 0, -180079972482, 0, -170793719332, 0, -60621600000, 0, -244406814874, 0, -9390284772, 0, 33796358694, 0, -1042524160, 0, -39731120000, 0, 76730279072, 0, 139794428880, 0, 61540804864, 0, 54350952360, 0, 10441907840, 0, -9960525728, 0, -30229537404, 0, -27960222400, 0, -19055284536, 0, -120868805120, 0, -252118445074, 0, -4510109744, 0, 478952504640, 0, 262165485464, 0, -6055584320, 0, -145636987320, 0, 249848066784, 0, -320489183268, 0, -88259462088, 0, 52086101100, 0, 128979657600, 0, 2462895008, 0, -161207420917, 0, 8045112240, 0, 59108441280, 0, 88404448874, 0, 103337733252, 0, 1695556020, 0, 273115437544, 0, -184953576320, 0, 161588431910, 0, 70467069542, 0, 4979457910, 0, -63846533400, 0, -75771878400, 0, -162028787148, 0, 226001195090, 0, 178424793228, 0, 153309938224, 0, 6456577120, 0, 159345835968, 0, -275304488, 0, 13706256090, 0, 226181467028, 0, -2358162400, 0, -550755842400, 0, -6682394600, 0, 342235299996, 0, 132531846830, 0, 61350853120, 0, 10493751294, 0, 101424640616, 0, -316576318500, 0, 111943931764, 0, 108271991680, 0, 275657017424, 0, -246995546400, 0, 277899884856, 0, -164343531758, 0, -48194752000, 0, 104388004658, 0, -20391867936, 0, 135290890260, 0, 177088876512, 0, -141542468800, 0, -21395862608, 0, 5913139152, 0, -2289813120, 0, -13845768646, 0, 56105104000, 0, 11934040274, 0, -267021314004, 0, 149766770600, 0, -124042241968, 0, 41820535680, 0, 48630486800, 0, -439375880078, 0, 4743072924, 0, 102586812480, 0, -43823788800, 0, -351304254000, 0, -73331099842, 0, -310138424754, 0, 43400400620, 0, -135798434400, 0, -161027772200, 0, 103000078992, 0, 172023746698, 0, 62714211238, 0, 200916437440, 0, -278987648, 0, -45130488744, 0, -345720879616, 0, 173106852952, 0, -132544631450, 0, -1501654686, 0, 200340874184, 0, 497401680872, 0, 25381751200, 0, 115004419840, 0, 254290433760, 0, -405834371180, 0, -26591390560, 0, 12258966092, 0, -2080674880, 0, -1296542268, 0, 663007383389, 0, -18534731148, 0, -89427409500, 0, 43081348800, 0, -148661968596, 0, 371675456280, 0, 376930725720, 0, -4511707376, 0, 89226681920, 0, -172074281614, 0, -3982209420, 0, -47397512464, 0, -174145103582, 0, 34908278750, 0, 137039744010, 0, 420538218148, 0, -3262529520, 0, -172668835612, 0, 28611168000, 0, 406212434232, 0, 116381358450, 0, 6639455456, 0, -153714561952, 0, 56071059200, 0, 152186262704, 0, 11893038180, 0, -308645329990, 0, -734650993440, 0, -70961116160, 0, 575735320202, 0, 6924659488, 0, 15694376600, 0, -109561366362, 0, -335628152960, 0, 110947642880, 0, -64619420864, 0, -416296324092, 0, -78730748092, 0, 123229953000, 0, 34849106344, 0, -294813904412, 0, 43071094178, 0, -415416756118, 0, -10983575040, 0, -59269567800, 0, 27874452718, 0, -436746524728, 0, -61146752328, 0, 59315608000, 0, -910440416160, 0, -307643771748, 0, -244965183008, 0, -1686104308, 0, 2586946560, 0, -112696572888, 0, 437564262036, 0, 418459000620, 0, -203064658400, 0, -162038098560, 0, 156299417862, 0, -775586806560, 0, -262106535544, 0, 217967060396, 0, 15014166200, 0, -416583602880, 0, -163790983026, 0, -147944238330, 0, -95784495440, 0, -345418599040, 0, -466923481442, 0, -3410939400, 0, -904641518880, 0, -369889183266, 0, -16959456640, 0, -50473912538, 0, 56096879360, 0, 2768377152, 0, -140548651320, 0, 31943723200, 0, -5669252872, 0, 21548355542, 0, -105501756704, 0, -30172717440, 0, 32125504000, 0, 293918960026, 0, 475640997740, 0, 183963279552, 0, -46615866731, 0, 242804743775, 0, -619374160032, 0, -581675423360, 0, 270173317448, 0, 18301739912, 0, -583383052800, 0, -28791599732, 0, 486634527888, 0, 233507594000, 0, -913651998, 0, 312003547840, 0, -246332640, 0, -156126189784, 0, 286496037688, 0, -462320888014, 0, 380097735040, 0, 452225774814, 0, -65864881920, 0, -20339631564, 0, -50482088760, 0, 158800438720, 0, 104720334000, 0, 22191082566, 0, 36265443500, 0, -485543147076, 0, -372661618450, 0, -68657463984, 0, 243686792160, 0, -545493267382, 0, 563657561688, 0, -408677380480, 0, -729143616448, 0, -437585519590, 0, 139572989688, 0, 970827200, 0, -103341303360, 0, -6995747718, 0, -417031552338, 0, -26522291520, 0, -30293734700, 0, -42544317120, 0, 113750582736, 0, -164731083736, 0, 322546701696, 0, 183515153754, 0, -2161444480, 0, 155601467196, 0, -43494408800, 0, 151766183744, 0, 1010947307760, 0, -346295664000, 0, -525581825100, 0, -81687337406, 0, 571280349958, 0, 29690460064, 0, 5262772480, 0, -56148992126, 0, 3108419456, 0, 110181212584, 0, -561008131720, 0, -145992960000, 0, 168820397516, 0, -44232543922, 0, 18269451336, 0, 557337565830, 0, 299917881600, 0, 35056734136, 0, -159720360096, 0, -395456216882, 0, 264680935848, 0, 202871369920, 0, -1333874049840, 0, -18299463178, 0, -107813195600, 0, 143780861580, 0, -148984641300, 0, 188312112072, 0, -19086822272, 0, -478254539720, 0, 1542465004828, 0, -1049082880, 0, 464017202632, 0, 456938292960, 0, 119361236106, 0, 736785175104, 0, 418253802240, 0, -339552398600, 0, 870806979184, 0, -73955125760, 0, -669771013262, 0, -1336492640, 0, -864316600816, 0, -470421208639, 0, 312010868160, 0, 409455259230, 0, -354307899520, 0, -91422507536, 0, -265203724786, 0, 17183999442, 0, 1383236200, 0, 13256784750, 0, -364717818036, 0, 389628769808, 0, -1780998944, 0, -144666451440, 0, -150422075520, 0, 110478359238, 0, -119855138580, 0, -736937020184, 0, 405647441510, 0, -287579860160, 0, -42983752952, 0, 311474836400, 0, 449466772052, 0, 783300880368, 0, -200448115200, 0, 51118513552, 0, -21608012626, 0, -38172603084, 0, 174714138088, 0, -515364098560, 0, -358294544174, 0, 7016904374, 0, -376388637740, 0, -731377644398, 0, -52246617500, 0, 473984640, 0, 758997908640, 0, -1044504640566, 0, 13308778788, 0, -182962717760, 0, 430023179420, 0, -85173588500, 0, -17625959376, 0, -452126906774, 0, -275308366080, 0, -153937980858, 0, -183390846022, 0, 386005439600, 0, 22384839932, 0, 52830172800, 0, 962511638116, 0, 903607565436, 0, 32565806880, 0, 15179323874, 0, -571502558720, 0, -259112500976, 0, 557237597168, 0, 1145751847200, 0, 9387995648, 0, -167284561400, 0, 328830663600, 0, 855529766124, 0, -12981658886, 0, -378964178410, 0, -332698041280, 0, -56600950424, 0, -111791334768, 0, 467551879996, 0, 336085862400, 0, -54421422720, 0, 367745382808, 0, -285041905962, 0, 376834635000, 0, 383546842800, 0, 592626169600, 0, 211392813240, 0, 126713720994, 0, 25587190604, 0, -919857266988, 0, -1058135961600, 0, 5504340320, 0, 16372708416, 0, -550901367746, 0, -396494229236, 0, 140433072000, 0, 634622883114, 0, 12792526400, 0, 482345078058, 0, 809811909900, 0, -8917713600, 0, -162435964320, 0, 966359042762, 0, -214685126712, 0, 415294556274, 0, 378931136640, 0, 144991065648, 0, 361740762036, 0, 13841287201, 0, 26215244520, 0, 247340768000, 0, 437488066956, 0, -793980825120, 0, -869590854710, 0, 64771301408, 0, 2463892480, 0, 443096143794, 0, 529984889852, 0, 35741945564, 0, 524633148928, 0, 95847304850, 0, 279827342324, 0, 131520891376, 0, -328603176000, 0, -380688862180, 0, -240876528640, 0, -1201775189766, 0, -31502112688, 0, 556725445218, 0, 232108082164, 0, -110385809920, 0, 111330963888, 0, -19790972128, 0, -298788048192, 0, -546164642880, 0, 547185287040, 0, -103317499600, 0, 818318475412, 0, -2658901184, 0, 168005577084, 0, 163438830720, 0, -239647258622, 0, 759456863536, 0, -303431667490, 0, 479433675910, 0, -25508241000, 0, -409032525604, 0, -528607733928, 0, 810182038552, 0, 11244831200, 0, -58620620800, 0, 636985502320, 0, 147903797028, 0, 149362282680, 0, -5769930446, 0, -273028192640, 0, -88019431920, 0, 89652773364, 0, 17564119568, 0, 62954679488, 0, -273622455040, 0, -5268692000, 0, -428618010600, 0, -320053864636, 0, -93947247240, 0, -384411325440, 0, 1104122214456, 0, -1959479998560, 0, 22108670550, 0, -618593006990, 0, -505229991200, 0, -291117893745, 0, -32353523814, 0, -1098828647508, 0, -338572296612, 0, -399931485120, 0, 2797711869216, 0, 1109928056078, 0, 430714612762, 0, -183976538032, 0, 76262847360, 0, 30624026010, 0, 265787683066, 0, -565504915352, 0, 23932351552, 0, 138487375040, 0, 533478332482, 0, 180443973496, 0, 565531395400, 0, -673956540720, 0, 111645635840, 0, -1159989355536, 0, 246540725032, 0, 408033390692, 0, 491225127368, 0, -881123472900, 0, 121982730724, 0, -1198933744366, 0, -15562872180, 0, -4460446774, 0, -208229299200, 0, -193731147600, 0, -90853467664, 0, -612931456424, 0, 405675523098, 0, 790501653760, 0, 92355641490, 0, -24526452512, 0, 9649348507, 0, -346942470652, 0, 536227024320, 0, 89939214720, 0, 534332447174, 0, 191279699366, 0, -132285309600, 0, 488097065280, 0, -1220192013122, 0, 189537703192, 0, 975773033580, 0, 92718390144, 0, -329823312000, 0, -569395505920, 0, 1760042917440, 0, 734882422916, 0, 661897853526, 0, 183514172160, 0, -59303844536, 0, 61335191400, 0, 373029163324, 0, -889792852020, 0, -544619659360, 0, 69262928072, 0, -1278844863800, 0, -1762934199120, 0, 120202333160, 0, -32871227840, 0, 967784397906, 0, 1048917954270, 0, -1107801116712, 0, 1285619356712, 0, 84985312000, 0, -152122892768, 0, 1333892000760, 0, 104795671400, 0, -99298810800, 0, 143093017100, 0, -956349728992, 0, -58798139504, 0, -719502852908, 0, -1495402442932, 0, 834549546240, 0, -137246180292, 0, 346666005694, 0, -200958400, 0, 387851214480, 0, -128755065600, 0, 196384590672, 0, 1416379084404, 0, 1345159568396, 0, 598205880360, 0, -594065110720, 0, 1631248619014, 0, -23546038992, 0, 1102446284152, 0, -686995455758, 0, 973415435520, 0, 133258248000, 0, 1858297476676, 0, 1456196387384, 0, 127157834650, 0, 283543081250, 0, -999090504064, 0, 651636403878, 0, 1216756668308, 0, -237072935712, 0, 214054973440, 0, 5545766688, 0, -2232351292320, 0, 1334871071334, 0, -485771982000, 0, -1089378560, 0, -181627531752, 0, 1697580210440, 0, -347369173788, 0, 27236128242, 0, -66279250560, 0, 1099633461040, 0, -17474474040, 0, -2081673329040, 0, 9156007634, 0, -15687338240, 0, -1163559320624, 0, -142492544000, 0, -248458060752, 0, 550558343192, 0, -1287957751300, 0, 299997615582, 0, -740491121692, 0, -1742418522288, 0, 26643266704, 0, -1114744985280, 0, 2007067798452, 0, -2239997462060, 0, -1510861697260, 0, -36356835172, 0, 448624896000, 0, 1193425560426, 0, -38980058184, 0, -103050943202, 0, -930374431034, 0, -833972198400, 0, 68479356610, 0, -558470439737, 0, 215074931356, 0, -112520447628, 0, 359435593920, 0, -24707427882, 0, 1532321781390, 0, 68869049200, 0, 447280786192, 0, 1319930244050, 0, 1462346130960, 0, 8223061568, 0, 137301019476, 0, 1641571070842, 0, -253691086880, 0, 367577741598, 0, -615873585624, 0, -795285929760, 0, 691521572872, 0, -563578390080, 0, 336629297200, 0, -1250627419440, 0, -1080291539948, 0, 54896397842, 0, 533251959040, 0, -47289392006, 0, 1064660627500, 0, -1456586790204, 0, 668857605682, 0, 28538606080, 0, 18245940128, 0, 470409784528, 0, 29945533680, 0, -900171872622, 0, -20402304000, 0, 814834519492, 0, -1983160849368, 0, -958784884416, 0, -1045073559090, 0, 1190383652160, 0, 1819676693476, 0, 282965930512, 0, 340428440506, 0, 530277292800, 0, -1087802951040, 0, 1950018218118, 0, 231561032800, 0, -2128122087072, 0, -1709967412992, 0, 389370197440, 0, 7901617548, 0, -891708474266, 0, -195642049280, 0, 826354539244, 0, -859114944000, 0, -1462061434104, 0, -876102134404, 0, -9410061056, 0, -152374706576, 0, 10814897500, 0, 991589021648, 0, 593117405376, 0, 325238538092, 0, -221537919078, 0, 470577009600, 0, 79411989600, 0, -1120315546730, 0, 1779273151656, 0, 560705431000, 0, -74420391680, 0, -91204379826, 0, -1798867869224, 0, 37318180200, 0, -1280869895018, 0, 1435279679360, 0, 394000487616, 0, 3443308558560, 0, -4633596604, 0, -104088425232, 0, -928769787840, 0, 43408326144, 0, -1579377029382, 0, -1852771861290, 0, -984008876352, 0, -298454298450, 0, 830773683600, 0, 53635532272, 0, -3034851419520, 0, -540932419480, 0, -491676291840, 0, 1034399535192, 0, 11282068504, 0, 1963217545616, 0, 462191520364, 0, -1221927840000, 0, -2464159587362, 0, -165598333012, 0]}